Alright, let's solve the expression step-by-step:
[tex]\[ 6 - [6 - 5(3 - 2 + (3 - 2))] \][/tex]
1. Begin with the innermost parentheses:
[tex]\[ (3 - 2) \][/tex]
This evaluates to:
[tex]\[ 1 \][/tex]
2. Substitute this result back into the expression:
[tex]\[ 6 - [6 - 5(3 - 2 + 1)] \][/tex]
3. Now evaluate the expression inside the next set of parentheses:
[tex]\[ 3 - 2 + 1 \][/tex]
This evaluates to:
[tex]\[ 2 \][/tex]
4. Substitute this result back into the expression:
[tex]\[ 6 - [6 - 5(2)] \][/tex]
5. Now evaluate the multiplication:
[tex]\[ 5 \times 2 \][/tex]
This evaluates to:
[tex]\[ 10 \][/tex]
6. Substitute this result back into the expression:
[tex]\[ 6 - [6 - 10] \][/tex]
7. Now evaluate the expression inside the brackets:
[tex]\[ 6 - 10 \][/tex]
This evaluates to:
[tex]\[ -4 \][/tex]
8. Substitute this result back into the expression:
[tex]\[ 6 - (-4) \][/tex]
9. Finally, perform the subtraction operation:
[tex]\[ 6 + 4 \][/tex]
This evaluates to:
[tex]\[ 10 \][/tex]
Therefore, the final result of the expression [tex]\( 6 - [6 - 5(3 - 2 + (3 - 2))] \)[/tex] is:
[tex]\[ 10 \][/tex]
